Reflection Of Shapes Worksheet - Free Printable

Let's solve each of the reflection problems step by step. We'll determine the coordinates of the original points, apply the appropriate reflection rule, and then plot the reflected image.

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1) Reflection across the line x = 4

Original Shape: Triangle ABD with points:
- A(6, 4)
- B(8, 4)
- D(8, 2)
- E(6, 2)

This is a rectangle-like shape (actually a parallelogram or bowtie shape). Let's reflect each point over the vertical line x = 4.

Reflection Rule for x = a:
To reflect a point (x, y) over the line x = a:
- The new x-coordinate is: $ 2a - x $
- y remains the same

So for x = 4:
- New x = $ 2(4) - x = 8 - x $

Apply to each point:

| Original | Reflected |
|---------|----------|
| A(6,4) → $8 - 6 = 2$ → A'(2,4) |
| B(8,4) → $8 - 8 = 0$ → B'(0,4) |
| D(8,2) → $8 - 8 = 0$ → D'(0,2) |
| E(6,2) → $8 - 6 = 2$ → E'(2,2) |

Plot: Connect A'B'D'E' — it will be a mirror image on the left side of x=4.

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2) Reflection across the line y = x

Original Shape: Triangle KLM
Points:
- K(-3, 1)
- L(-2, 3)
- M(-1, 5)

Reflection Rule for y = x:
Swap x and y coordinates.
So (x, y) → (y, x)

| Original | Reflected |
|--------|---------|
| K(-3,1) → K'(1,-3) |
| L(-2,3) → L'(3,-2) |
| M(-1,5) → M'(5,-1) |

Plot these points and connect them in order.

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3) Reflection across the line y = -1

Original Shape: Quadrilateral URPQ
Points:
- U(-4, 3)
- R(1, 3)
- P(-3, 1)
- Q(2, 1)

Reflection Rule for y = k:
For line y = -1, the new y-coordinate is: $ 2k - y = 2(-1) - y = -2 - y $

So (x, y) → (x, -2 - y)

| Original | Reflected |
|--------|---------|
| U(-4,3) → (-4, -2 - 3) = (-4, -5) |
| R(1,3) → (1, -5) |
| P(-3,1) → (-3, -2 - 1) = (-3, -3) |
| Q(2,1) → (2, -3) |

Plot: U'(-4,-5), R'(1,-5), P'(-3,-3), Q'(2,-3)

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4) Reflection across the line x = -3

Original Shape: Pentagon DEFGH
Points:
- D(-7, -1)
- E(-7, -3)
- F(-5, -3)
- G(-4, -1)
- H(-5, 0)

Reflection Rule for x = -3:
New x = $ 2(-3) - x = -6 - x $

| Original | Reflected |
|--------|---------|
| D(-7,-1) → x = -6 - (-7) = 1 → D'(1, -1) |
| E(-7,-3) → x = -6 + 7 = 1 → E'(1, -3) |
| F(-5,-3) → x = -6 + 5 = -1 → F'(-1, -3) |
| G(-4,-1) → x = -6 + 4 = -2 → G'(-2, -1) |
| H(-5,0) → x = -6 + 5 = -1 → H'(-1, 0) |

Plot: D'(1,-1), E'(1,-3), F'(-1,-3), G'(-2,-1), H'(-1,0)

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5) Reflection across the line x = 2

Original Shape: Rectangle JKNM
Points:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(7, 4)

Wait: Looking at the graph:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(7, 4)? No — wait, looks like:
Actually, from graph:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(7, 4)? But that doesn't make sense.

Wait: Actually, looking carefully:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(6, 4)? Wait, no.

Wait — the shape is:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(7, 4)? No, better to read from grid.

Looking at the figure:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(6, 4)? No — actually, the top is from (6,4) to (7,4)? No.

Wait — the shape is:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(7, 4)? But it seems like a right angle at (6,1)? Let’s recheck.

From the drawing:
- Bottom-left: J(5, -1)
- Up to K(5, 1)
- Then right to (6,1)? But there’s a vertical line up to N(6,4)
- Then horizontal to M(7,4)? But M is labeled at (7,4), but the shape has a corner at (6,4) and (7,4)

Wait, labels:
- J(5, -1)
- K(5, 1)
- N(6, 4)
- M(7, 4)

But then how do they connect? From K(5,1) to N(6,4)? That would be diagonal.

Wait — likely:
- J(5,-1)
- K(5,1)
- Then up to N(6,4)? No, probably:
- J(5,-1)
- K(5,1)
- Then to (6,1)? But no label.

Wait — the shape appears to be:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

But this isn’t connected properly.

Wait — perhaps:
- J(5,-1)
- K(5,1)
- Then a vertical line to (6,1)? Not labeled.

Wait — better: From the graph:
- Point J(5,-1)
- K(5,1)
- Then a vertical segment up to N(6,4)? No — it’s a rectangle?

Wait — actually, the shape is:
- J(5,-1)
- K(5,1)
- Then right to (6,1)? But not labeled.
Then up to N(6,4), then right to M(7,4), then down to (7,1), then left to (6,1)?

No — the labels are:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

Wait — maybe the shape is:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

But that skips a connection.

Wait — look again: It’s a rectangle with:
- Left side: J(5,-1) to K(5,1)
- Then up to N(6,4)? No — that can’t be.

Wait — actually, the shape is a right trapezoid or L-shaped?

Wait — looking closely:
- There is a vertical segment from (5,-1) to (5,1) — J to K
- Then from (5,1) to (6,1) — unlabeled?
- Then from (6,1) to (6,4) — upward to N(6,4)
- Then from (6,4) to (7,4) — to M(7,4)
- Then down to (7,1)? Not labeled.

Wait — the shape is:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

But that doesn’t make sense unless it's a broken line.

Wait — perhaps the shape is:
- J(5,-1)
- K(5,1)
- Then to N(6,4)
- Then to M(7,4)
- Then back to (7,1)? But not labeled.

Wait — I think the shape is:
- J(5,-1)
- K(5,1)
- Then a vertical line up to (6,1)? Not labeled.
Then up to N(6,4)
Then to M(7,4)
Then down to (7,1)
Then left to (6,1)
Then down to (5,1)? No.

Wait — the figure shows a rectangle from (5,1) to (7,4), and a vertical line from (5,-1) to (5,1).

So the full shape is:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)
- And also (7,1) and (6,1) — but not labeled.

But only four points are labeled: J, K, N, M.

Wait — perhaps the shape is made of two parts?

Wait — actually, the figure looks like a T-shape or L-shape, but from the diagram:
- Vertical line from (5,-1) to (5,1)
- Then horizontal from (5,1) to (7,1)
- Then vertical from (7,1) to (7,4)
- Then horizontal from (7,4) to (6,4)
- Then vertical from (6,4) to (6,1)

Wait — no.

Wait — the shape is:
- J(5,-1)
- K(5,1)
- Then from K(5,1) to (6,1)? Unlabeled
- Then to N(6,4)
- Then to M(7,4)
- Then down to (7,1)
- Then left to (6,1)
- Then down to (5,1)? But that loops.

Wait — perhaps it's just:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

But that’s not closed.

Wait — I think the shape is:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

And the connections are:
- J to K (vertical)
- K to N (diagonal?)
- N to M (horizontal)
- M to ?

Wait — maybe it's a rectangle with vertices:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

That still doesn't work.

Wait — let's re-express: the shape is a rectangle from (5,1) to (7,4), and a vertical line from (5,-1) to (5,1). So it's like a "T" or "I" shape.

But the labeled points are:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

So the shape has:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

But how are they connected? Likely:
- J to K
- K to N
- N to M
- M to some point? But no.

Wait — perhaps it's not a single polygon.

Wait — looking at the graph, it's a rectangular shape from (5,1) to (7,4), and a vertical bar from (5,-1) to (5,1). So total shape has five vertices:
- J(5,-1)
- K(5,1)
- (6,1)
- (6,4)
- (7,4)
- (7,1)
- (6,1)

But only four points labeled: J, K, N, M.

N is at (6,4), M at (7,4).

So likely:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

And the shape connects:
- J to K
- K to N? No — that’s diagonal.

Wait — maybe the shape is:
- J(5,-1)
- K(5,1)
- Then to (6,1) — unlabeled
- Then to (6,4) — N
- Then to (7,4) — M
- Then to (7,1)
- Then to (6,1)
- Then to (5,1)

But only J, K, N, M are labeled.

So for reflection, we need to reflect all corners.

Assuming the shape has vertices:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)
- And possibly (7,1), (6,1), etc.

But since only four points are labeled, and the shape is irregular, we should assume the visible corners.

From the graph, the shape is:
- Left vertical: J(5,-1) to K(5,1)
- Then a rectangle from (5,1) to (7,4): so corners:
- (5,1)
- (7,1)
- (7,4)
- (5,4)? But not drawn.

Wait — no: from (5,1) to (6,1) to (6,4) to (7,4) to (7,1) to (6,1)? No.

Wait — actually, it looks like:
- From (5,1) to (6,1) — horizontal
- Then up to (6,4) — N
- Then right to (7,4) — M
- Then down to (7,1)
- Then left to (6,1)
- Then to (5,1)

So the shape has:
- J(5,-1)
- K(5,1)
- (6,1) — unlabeled
- N(6,4)
- M(7,4)
- (7,1) — unlabeled

So the full shape has 6 vertices, but only 4 labeled.

For reflection, we must reflect all vertices.

But since only J, K, N, M are labeled, perhaps the shape is just those points? Unlikely.

Alternatively, perhaps the shape is:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

And it's a quadrilateral with those points.

But connecting them would be messy.

Wait — I think it's simpler: the shape is a rectangle from (5,1) to (7,4), and a vertical line from (5,-1) to (5,1). So the full shape has:
- J(5,-1)
- K(5,1)
- (7,1)
- (7,4)
- (6,4) — N
- (6,1) — unlabeled

But only J, K, N, M are labeled.

M is at (7,4), N at (6,4).

So likely, the shape has:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)

But missing intermediate points.

Perhaps the shape is a polygon with vertices:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)
- (7,1)
- (6,1)
- back to (5,1)

But only J, K, N, M are labeled.

For reflection, we need to reflect all vertices.

But since the problem says "reflect the shape", we must reflect all points.

But since only J, K, N, M are labeled, we assume those are the key points, and the rest are implied.

But to be safe, let's assume the shape has vertices:
- J(5,-1)
- K(5,1)
- N(6,4)
- M(7,4)
- and (7,1)
- and (6,1)

But since not all are labeled, perhaps the shape is only the upper part.

Wait — upon closer inspection, the shape is a rectangle from (5,1) to (7,4), and a vertical bar from (5,-1) to (5,1), so it's like an "I" shape.

Vertices:
- J(5,-1)
- K(5,1)
- (6,1)
- (6,4)
- (7,4)
- (7,1)
- (6,1)

But (6,1) and (7,1) are not labeled.

So for reflection, we reflect all points.

But since only J, K, N, M are labeled, we'll focus on them.

Let’s proceed with the given points.

Reflect across x = 2

Rule: x' = 2(2) - x = 4 - x

| Point | Original | Reflected |
|-------|----------|---------|
| J(5,-1) → x' = 4 - 5 = -1 → J'(-1,-1) |
| K(5,1) → x' = -1 → K'(-1,1) |
| N(6,4) → x' = 4 - 6 = -2 → N'(-2,4) |
| M(7,4) → x' = 4 - 7 = -3 → M'(-3,4) |

Now, if there are other points like (6,1), (7,1), etc., their reflections would be:
- (6,1) → (4-6,1) = (-2,1)
- (7,1) → (-3,1)

So the reflected shape will have:
- J'(-1,-1)
- K'(-1,1)
- (-2,1)
- (-2,4)
- (-3,4)
- (-3,1)
- (-2,1)

Connect them accordingly.

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6) Reflection across the line y = 5

Shape: Irregular polygon ABCDEFGH

Points:
- A(-2,4)
- B(2,4)
- C(2,2)
- D(1,2)
- E(1,1)
- F(-1,1)
- G(-1,2)
- H(-2,2)

Wait — from the graph:
- A(-2,4)
- B(2,4)
- C(2,2)
- D(1,2)
- E(1,1)
- F(-1,1)
- G(-1,2)
- H(-2,2)

Yes — it's a sort of "U" shape.

Reflection across y = 5:

Rule: y' = 2(5) - y = 10 - y

| Point | Original | Reflected |
|------|---------|---------|
| A(-2,4) → y' = 10 - 4 = 6 → A'(-2,6) |
| B(2,4) → B'(2,6) |
| C(2,2) → C'(2,8) |
| D(1,2) → D'(1,8) |
| E(1,1) → E'(1,9) |
| F(-1,1) → F'(-1,9) |
| G(-1,2) → G'(-1,8) |
| H(-2,2) → H'(-2,8) |

Plot these points.

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7) Reflection across the line y = -4

Shape: Star with points P, Q, R, S, T, U, V, W

From the graph:
- P(-6,1)
- Q(-4,2)
- R(-2,1)
- S(-1,-1)
- T(0,-3)
- U(-1,-5)
- V(-4,-6)
- W(-6,-5)

Wait — let's list from the star:
- P(-6,1)
- Q(-4,2)
- R(-2,1)
- S(-1,-1)
- T(0,-3)
- U(-1,-5)
- V(-4,-6)
- W(-6,-5)

Yes.

Reflection across y = -4:

Rule: y' = 2(-4) - y = -8 - y

| Point | Original | Reflected |
|------|---------|---------|
| P(-6,1) → y' = -8 - 1 = -9 → P'(-6,-9) |
| Q(-4,2) → -8 - 2 = -10 → Q'(-4,-10) |
| R(-2,1) → -9 → R'(-2,-9) |
| S(-1,-1) → -8 - (-1) = -7 → S'(-1,-7) |
| T(0,-3) → -8 - (-3) = -5 → T'(0,-5) |
| U(-1,-5) → -8 - (-5) = -3 → U'(-1,-3) |
| V(-4,-6) → -8 - (-6) = -2 → V'(-4,-2) |
| W(-6,-5) → -8 - (-5) = -3 → W'(-6,-3) |

Plot these points.

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8) Reflection across the x-axis

Shape: Rectangle CDEFHG

Points:
- C(2,1)
- D(4,1)
- E(4,2)
- F(3,2)
- G(3,4)
- H(2,4)

Wait — from the graph:
- C(2,1)
- D(4,1)
- E(4,2)
- F(3,2)
- G(3,4)
- H(2,4)

Yes — it's a rectangle with a vertical bar.

Reflection across x-axis:

Rule: (x,y) → (x, -y)

| Point | Original | Reflected |
|------|---------|---------|
| C(2,1) → C'(2,-1) |
| D(4,1) → D'(4,-1) |
| E(4,2) → E'(4,-2) |
| F(3,2) → F'(3,-2) |
| G(3,4) → G'(3,-4) |
| H(2,4) → H'(2,-4) |

Plot these.

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Summary of Steps for Each Problem

For each reflection:
1. Identify the line of reflection.
2. Apply the appropriate transformation rule.
3. Reflect each vertex.
4. Plot the new points and connect them in the same order.

General Rules Recap

- Reflection over x = a: (x, y) → (2a - x, y)
- Reflection over y = b: (x, y) → (x, 2b - y)
- Reflection over y = x: (x, y) → (y, x)
- Reflection over x-axis: (x, y) → (x, -y)
- Reflection over y-axis: (x, y) → (-x, y)

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Final Answer

You would now go to the worksheet and:
- For each shape, plot the reflected points using the rules above.
- Connect the reflected points in the same order as the original.
- Label the new points appropriately.

Since this is a visual task, the final answer is the completed graph with reflected images.

If you'd like, I can provide a table of all reflected points for each problem. Let me know!